Question

Answer Check!! Calculus!! Medal!!
A stone is thrown upward with a speed of 30 feet per second from the edge of a cliff 200 feet above the ground. What is the speed of the stone when it hits the ground? Use acceleration due to gravity as –32 feet per second squared and approximate your answer to 3 decimal places.

Answer 1

a(t) = -32

v(t) = ∫a(t) dt
v(t) = ∫-32 dt
v(t) = -32t + v₀
v(t) = -32t + 30

h(t) = ∫v(t) dt
h(t) = ∫ -32t + 30 dt
h(t) = -16t² + 30t + h₀
h(t) = -16t² + 30t + 200
The stone hits the ground when its height is 0:
0 = -16t² + 30t + 200
By the quadratic formula, positive t = 4.5952 seconds

speed = |v(t)| = |v(4.5952)| = 117.046 ft/sec

Answer 2

I think it looks good.

Answer 3

Thanks for you input :)